Recent zbMATH articles in MSC 91A https://zbmath.org/atom/cc/91A 2022-06-24T15:10:38.853281Z Unknown author Werkzeug On semantic gamification https://zbmath.org/1485.03255 2022-06-24T15:10:38.853281Z "Quintana, Ignacio Ojea" https://zbmath.org/authors/?q=ai:quintana.ignacio-ojea Summary: The purpose of this essay is to study the extent in which the semantics for different logical systems can be represented game theoretically. I will begin by considering different definitions of what it means to gamify a semantics, and show completeness and limitative results. In particular, I will argue that under a proper definition of gamification, all finitely algebraizable logics can be gamified, as well as some infinitely algebraizable ones (like Łukasiewicz) and some non-algebraizable (like intuitionistic and van Fraassen supervaluation logic). For the entire collection see [Zbl 1416.03005]. Game-perfect semiorientations of forests https://zbmath.org/1485.05113 2022-06-24T15:10:38.853281Z "Andres, Stephan Dominique" https://zbmath.org/authors/?q=ai:andres.stephan-dominique "Charpentier, Clément" https://zbmath.org/authors/?q=ai:charpentier.clement "Fong, Wai Lam" https://zbmath.org/authors/?q=ai:fong.wai-lam Summary: We consider digraph colouring games where two players, Alice and Bob, alternately colour vertices of a given digraph $$D$$ with a colour from a given colour set in a feasible way. The game ends when such move is not possible any more. Alice wins if every vertex is coloured at the end, otherwise Bob wins. The smallest size of a colour set such that Alice has a winning strategy is the game chromatic number of $$D$$. The digraph $$D$$ is game-perfect if, for every induced subdigraph $$H$$ of $$D$$, the game chromatic number of $$H$$ equals the size of the largest symmetric clique of $$H$$. In the strong game, colouring a vertex is feasible if its colour is different from the colours of its in-neighbours. In the weak game, colouring a vertex is feasible unless it creates a monochromatic directed cycle. There are six variants for each game, which specify the player who begins and whether skipping is allowed for some player. For all six variants of both games, we characterise the class of game-perfect semiorientations of forests by a set of forbidden induced subdigraphs and by an explicit structural description. The domination game played on diameter 2 graphs https://zbmath.org/1485.05114 2022-06-24T15:10:38.853281Z "Bujtás, Csilla" https://zbmath.org/authors/?q=ai:bujtas.csilla "Iršič, Vesna" https://zbmath.org/authors/?q=ai:irsic.vesna "Klavžar, Sandi" https://zbmath.org/authors/?q=ai:klavzar.sandi "Xu, Kexiang" https://zbmath.org/authors/?q=ai:xu.kexiang Summary: Let $$\gamma_g(G)$$ be the game domination number of a graph $$G$$. It is proved that if $$\operatorname{diam}(G) = 2$$, then $$\gamma_g(G) \le \left\lceil \frac{n(G)}{2} \right\rceil - \left\lfloor \frac{n(G)}{11}\right\rfloor$$. The bound is attained: if $$\operatorname{diam}(G) = 2$$ and $$n(G) \le 10$$, then $$\gamma_g(G) = \left\lceil \frac{n(G)}{2} \right\rceil$$ if and only if $$G$$ is one of seven sporadic graphs with $$n(G)\le 6$$ or the Petersen graph, and there are exactly ten graphs of diameter 2 and order 11 that attain the bound. Meyniel extremal families of abelian Cayley graphs https://zbmath.org/1485.05115 2022-06-24T15:10:38.853281Z "Hasiri, Fatemeh" https://zbmath.org/authors/?q=ai:hasiri.fatemeh "Shinkar, Igor" https://zbmath.org/authors/?q=ai:shinkar.igor Summary: We study the game of Cops and Robbers, where cops try to capture a robber on the vertices of a graph. Meyniel's conjecture states that for every connected graph $$G$$ on $$n$$ vertices, the cop number of $$G$$ is upper bounded by $$O(\sqrt{n})$$. That is, for every graph $$G$$ on $$n$$ vertices $$O(\sqrt{n})$$ cops suffice to catch the robber. We present several families of abelian Cayley graphs that are Meyniel extremal, i.e., graphs whose cop number is $$O(\sqrt{n})$$. This proves that the $$O(\sqrt{n})$$ upper bound for Cayley graphs proved by \textit{P. Bradshaw} [Discrete Math. 343, No. 1, Article ID 111546, 5 p. (2020; Zbl 1429.05088)] is tight. In particular, this shows that Meyniel's conjecture, if true, is tight even for abelian Cayley graphs. In order to prove the result, we construct Cayley graphs on $$n$$ vertices with $$\Omega (\sqrt{n})$$ generators that are $$K_{2,3}$$-free. This shows that the Kövári, Sós, and Turán theorem [\textit{T. Kövári} et al., Colloq. Math. 3, 50--57 (1954; Zbl 0055.00704)], stating that any $$K_{2,3}$$-free graph of $$n$$ vertices has at most $$O(n^{3/2})$$ edges, is tight up to a multiplicative constant even for abelian Cayley graphs. Cyber kittens, or some first steps towards categorical cybernetics https://zbmath.org/1485.18025 2022-06-24T15:10:38.853281Z "St. Clere Smithe, Toby" https://zbmath.org/authors/?q=ai:st-clere-smithe.toby Recent work in applied category theory has developed categorical frameworks for open games and for open dynamical systems. The present paper attempts the ambitious goal of developing a categorical notion of \textit{cybernetic system} that would unify both of the previous, and is expected to capture characteristic features of cybernetic systems, such as the existence of internal regulatory mechanisms ensuring the system's stability. The title seems to indicate that this project is in a juvenile stage: a kitten will grow up and become a cat(egory). Section 2 introduces Bayesian lenses and optics. Section 3 introduces a novel generalization of open games and sketches how various optimization problems in cybernetics (maximum likelihood game, variational autoencoder game) can be formulated within this framework. Section 4 then adds the dynamical aspect and defines open cybernetic systems. Again various examples from cybernetics are announced, such as active inference, and it is suggested that the optical structure of Bayesian inference justifies the bidirectionality of cortical circuits. While the developments of this paper seem very sensible in terms of the big picture, the details often remain unclear. For example, Section 2 makes assumptions on an unspecified category of measurable spaces'' (Cartesian closure, Bayesian inverses) that are not known to be jointly satisfiable; Definition 3.2 refers to the monoidal unit $$I$$ in the underlying actegories'', although actegories do not have units; proofs are delegated to a follow-up paper; etc. For the entire collection see [Zbl 1466.68028]. Reviewer: Tobias Fritz (Innsbruck) Dynamics analysis of an online gambling spreading model on scale-free networks https://zbmath.org/1485.37089 2022-06-24T15:10:38.853281Z "Kong, Yu" https://zbmath.org/authors/?q=ai:kong.yu "Li, Tao" https://zbmath.org/authors/?q=ai:li.tao.3 "Wang, Yuanmei" https://zbmath.org/authors/?q=ai:wang.yuanmei "Cheng, Xinming" https://zbmath.org/authors/?q=ai:cheng.xinming "Wang, He" https://zbmath.org/authors/?q=ai:wang.he|wang.he.1 "Lei, Yangmei" https://zbmath.org/authors/?q=ai:lei.yangmei Summary: Nowadays, online gambling has a great negative impact on the society. In order to study the effect of people's psychological factors, anti-gambling policy, and social network topology on online gambling dynamics, a new \textit{SHGD} (susceptible-hesitator-gambler-disclaimer) online gambling spreading model is proposed on scale-free networks. The spreading dynamics of online gambling is studied. The basic reproductive number $$R_0$$ is got and analyzed. The basic reproductive number $$R_0$$ is related to anti-gambling policy and the network topology. Then, gambling-free equilibrium $$E_0$$ and gambling-prevailing equilibrium $$E_{+}$$ are obtained. The global stability of $$E_0$$ is analyzed. The global attractivity of $$E_{+}$$ and the persistence of online gambling phenomenon are studied. Finally, the theoretical results are verified by some simulations. Gradient methods for solving zero-sum linear-quadratic differential games https://zbmath.org/1485.49045 2022-06-24T15:10:38.853281Z "Gibali, Aviv" https://zbmath.org/authors/?q=ai:gibali.aviv "Kelis, Oleg" https://zbmath.org/authors/?q=ai:kelis.oleg Summary: We focus on a zero-sum linear-quadratic differential game. The main feature of this game is that the weight matrix of the minimizer's control cost in the cost functional is singular. Due to this singularity, the game cannot be solved either by applying the Isaacs MinMax principle, or the Bellman-Isaacs equation approach. \textit{V. Y. Glizer} and the second author [Solution of a zero-sum linear quadratic differential game with singular control cost of minimiser'', J. Control Decis. 2, 155--184 (2015)] studied appropriate diagonal singular form of the weight matrix in the cost functional. In this paper we study the case where the weight matrix has general singular form. This means that only a part of coordinates of the minimizer's control is singular, while the rest of coordinates are regular. As application, we introduce a pursuit-evasion differential game and propose two gradient methods for solving this game, the Arrow-Hurwicz-Uzawa and Korpelevich's extragradient method. We present numerical illustrations which demonstrate the procedures performances. Equilibrium price formation with a major player and its mean field limit https://zbmath.org/1485.49047 2022-06-24T15:10:38.853281Z "Fujii, Masaaki" https://zbmath.org/authors/?q=ai:fujii.masaaki "Takahashi, Akihiko" https://zbmath.org/authors/?q=ai:takahashi.akihiko Summary: In this article, we consider the problem of equilibrium price formation in an incomplete securities market consisting of one major financial firm and a large number of minor firms. They carry out continuous trading \textit{via} the securities exchange to minimize their cost while facing idiosyncratic and common noises as well as stochastic order flows from their individual clients. The equilibrium price process that balances demand and supply of the securities, including the functional form of the price impact for the major firm, is derived endogenously both in the market of finite population size and in the corresponding mean field limit. Provenance analysis for logic and games https://zbmath.org/1485.68151 2022-06-24T15:10:38.853281Z "Grädel, Erich" https://zbmath.org/authors/?q=ai:gradel.erich "Tannen, Val" https://zbmath.org/authors/?q=ai:tannen.val Summary: A model-checking computation checks whether a given logical sentence is true in a given finite structure. Provenance analysis abstracts from such a computation mathematical information on how the result depends on the atomic data that describe the structure. In database theory, provenance analysis by interpretations in commutative semirings has been rather successful for positive query languages (such as unions of conjunctive queries, positive relational algebra, and Datalog). However, it did not really offer an adequate treatment of negation or missing information. Here we propose a new approach for the provenance analysis of logics with negation, such as first-order logic and fixed-point logics. It is closely related to a provenance analysis of the associated model-checking games, and based on new semirings of dual-indeterminate polynomials or dual-indeterminate formal power series. These are obtained by taking quotients of traditional provenance semirings by congruences that are generated by products of positive and negative provenance tokens. Beyond the use for model-checking problems in logics, provenance analysis of games is of independent interest. Provenance values in games provide detailed information about the number and properties of the strategies of the players, far beyond the question whether or not a player has a winning strategy from a given position. Complexity analysis of pricing, service level, and emission reduction effort in an e-commerce supply chain under different power structures https://zbmath.org/1485.90016 2022-06-24T15:10:38.853281Z "Xi, Xuan" https://zbmath.org/authors/?q=ai:xi.xuan "Zhang, Yulin" https://zbmath.org/authors/?q=ai:zhang.yulin|zhang.yulin.1 Complex dynamics of pricing game model in a dual-channel closed-loop supply chain with delay decision https://zbmath.org/1485.90017 2022-06-24T15:10:38.853281Z "Zhang, Yuhao" https://zbmath.org/authors/?q=ai:zhang.yuhao "Zhang, Tao" https://zbmath.org/authors/?q=ai:zhang.tao.2|zhang.tao.5|zhang.tao.1|zhang.tao.6|zhang.tao.4 Joining strategies under two kinds of games for a multiple vacations retrial queue with $$N$$-policy and breakdowns https://zbmath.org/1485.90027 2022-06-24T15:10:38.853281Z "Wang, Zhen" https://zbmath.org/authors/?q=ai:wang.zhen.3 "Liu, Liwei" https://zbmath.org/authors/?q=ai:liu.liwei "Shao, Yuanfu" https://zbmath.org/authors/?q=ai:shao.yuanfu "Zhao, Yiqiang Q." https://zbmath.org/authors/?q=ai:zhao.yiqiang-q Summary: Motivated by cost control and information guidance, in this work, we study a multiple vacations retrial queue with $$N$$-policy and breakdowns. This service system has the characteristics that there is no waiting space in front of the server and the waiting list is virtual. If the arriving customer finds that the system is available, he immediately receives the complete service. Otherwise, the customer leaves the system or joins the orbit (virtual waiting list). For cost control, the system is activated only when the current vacation is completed and at least $$N$$ customers are waiting in the system, otherwise, the server continues to the next vacation until the number of customers in the system is not less than $$N$$. Two types of customer joining cases apply to this paper, i.e., non-cooperative customers aim to optimize individual interests, and the social planner in the cooperative case considers the profit of the whole service system. The equilibrium joining strategy for the non-cooperative case and the socially optimal joining strategy for the cooperative case are determined. Since it is difficult to obtain analytical characterization, an improved particle swarm optimization (PSO) algorithm is used to explore the impact of system parameters on the profit of the service provider. At the same time, a large number of numerical experiments visualize the influence of parameters on the system. Overtaking optimality in a discrete-time advertising game https://zbmath.org/1485.90059 2022-06-24T15:10:38.853281Z "Rilwan, Jewaidu" https://zbmath.org/authors/?q=ai:rilwan.jewaidu "Kumam, Poom" https://zbmath.org/authors/?q=ai:kumam.poom "Ahmed, Idris" https://zbmath.org/authors/?q=ai:ahmed.idris Summary: In this paper, advertising competition among $$m$$ firms is studied in a discrete-time dynamic game framework. Firms maximize the present value of their profits which depends on their advertising strategy and their market share. The evolution of market shares is determined by the firms' advertising activities. By employing the concept of the discrete-time potential games of \textit{D. González-Sánchez} and \textit{O. Hernández-Lerma} [Discrete-time stochastic control and dynamic potential games. The Euler-equation approach. New York, NY: Springer (2013; Zbl 1344.93001)], we derived an explicit formula for the Nash equilibrium (NE) of the game and obtained conditions for which the NE is an overtaking optimal. Moreover, we analyze the asymptotic behavior of the overtaking NE where the convergence towards a unique steady state (turnpike) is established. Selfish bin packing with parameterized punishment https://zbmath.org/1485.90120 2022-06-24T15:10:38.853281Z "Zhang, Weiwei" https://zbmath.org/authors/?q=ai:zhang.weiwei "Gao, Alin" https://zbmath.org/authors/?q=ai:gao.alin "Gai, Ling" https://zbmath.org/authors/?q=ai:gai.ling Summary: In this paper we consider the problem of selfish bin packing with parameterized punishment. Different from the classical bin packing problem, each item to be packed belongs to a selfish agent, who wants to maximize his utility by selecting an appropriate bin. The utility of the agent is defined as the total size of the items sharing the same bin with its item. If an item moves unilaterally to another bin, it may have to pay the punishment. A parameter is defined such that the items are classified whether or not they are fit for the punishment. We study three versions of punishment-full, expansile and partial punishment, and prove the corresponding bounds of $$PoA^1$$ (Price of Anarchy). For the entire collection see [Zbl 1464.68025]. Auction theory. Introductory exercises with answer keys https://zbmath.org/1485.91003 2022-06-24T15:10:38.853281Z "Choi, Pak-Sing" https://zbmath.org/authors/?q=ai:choi.pak-sing "Munoz-Garcia, Felix" https://zbmath.org/authors/?q=ai:munoz-garcia.felix Publisher's description: This textbook provides a short introduction to auction theory through exercises with detailed answer keys. Focusing on practical examples, this textbook offers over 80 exercises that predict bidders' equilibrium behaviour in different auction formats, along with the seller's strategic incentives to organize one auction format over the other. The book emphasizes game-theoretic tools, so students can apply similar tools to other auction formats. Also included are several exercises based on published articles, with the model reduced to its main elements and the question divided into several easy-to-answer parts. Little mathematical background in algebra and calculus is assumed, and most algebraic steps and simplifications are provided, making the text ideal for upper undergraduate and graduate students. The book begins with a discussion of second-price auctions, which can be studied without using calculus, and works through progressively more complicated auction scenarios: first-price auctions, all-pay auctions, third-price auctions, the Revenue Equivalence principle, common-value auctions, multi-unit auctions, and procurement auctions. Exercises in each chapter are ranked according to their difficulty, with a letter (A--C) next to the exercise title, which allows students to pace their studies accordingly. The authors also offer a list of suggested exercises for each chapter, for instructors teaching at varying levels: undergraduate, Masters, Ph.D. Providing a practical, customizable approach to auction theory, this textbook is appropriate for students of economics, finance, and business administration. This book may also be used for related classes such as game theory, market design, economics of information, contract theory, or topics in microeconomics. Network games, control and optimization. 10th international conference, NetGCooP 2020, Cargèse, Corsica, France, September 22--24, 2021. Proceedings https://zbmath.org/1485.91006 2022-06-24T15:10:38.853281Z This book constitutes the conference proceedings of the 10th International Conference on Network Games, Control and Optimization, NETGCOOP 2020, held in Cargèse, Corsica, France, in September 2021*. The 12 full papers and 16 short papers were carefully reviewed and selected from 44 submissions. The papers are organized in the following topical sections: game theory and iterative algorithms applied to wireless communication; stochastic models for network performance analysis; game theory in mobile and wireless networks; scheduling and resource allocation problems in networks; advance in game theory; social network; electrical network. * The conference was postponed to 2021 due to the COVID-19 pandemic. The articles of this volume will be reviewed individually. For the preceding conference see [Zbl 1409.91007]. Local and global analysis of a nonlinear duopoly game with heterogeneous firms https://zbmath.org/1485.91007 2022-06-24T15:10:38.853281Z "Askar, Sameh" https://zbmath.org/authors/?q=ai:askar.sameh-s Summary: In this paper, we introduce a nonlinear duopoly game whose players are heterogeneous and their inverse demand functions are derived from a more general isoelastic demand. The game is modeled by a discrete time dynamic system whose Nash equilibrium point is unique. The conditions of local stability of Nash point are calculated. It becomes unstable via two types of bifurcations: flip and Neimark-Sacker. Some local and global numerical investigations are performed to show the dynamic behavior of game's system. We show that the system is noninvertible and belongs to $$Z_2-Z_0$$ type. We also show some multistability aspects of the system including basins of attraction and regions known as lobes. On existence of best proximity pairs and a generalization of Nash equilibriums https://zbmath.org/1485.91008 2022-06-24T15:10:38.853281Z "Kosuru, G. Sankara Raju" https://zbmath.org/authors/?q=ai:kosuru.g-sankara-raju Summary: We consider a constrained $$m$$-person game, in which each player has two strategy spaces and two pay-off functions, namely, a~manufacturing pay-off function and a~selling pay-off function. In this paper, we give sufficient conditions for the existence of an equilibrium pair which minimizes the manufacturing pay-off and maximizes the selling pay-off for each player. To prove the existence of such an equilibrium, we introduce a~notion of relatively upper semi-continuous mapping and therein prove the existence of a best proximity pair. Group formation in a dominance-seeking contest https://zbmath.org/1485.91009 2022-06-24T15:10:38.853281Z "Lee, Dongryul" https://zbmath.org/authors/?q=ai:lee.dongryul "Kim, Pilwon" https://zbmath.org/authors/?q=ai:kim.pilwon Summary: We study a group formation game. Players with different strengths form groups before expending effort to win a prize. The prize has the nature of the reward for outdoing in competition such as holding a dominant position among players or being recognized as a dominant status. So, it has the nature of public goods within a winning group (group-specific public goods). In open membership game, we find that a single player stays alone and the others form a group together in equilibrium. The stand-alone player can be anyone except for the first and second strongest players in the contest. However, strong (Nash) equilibrium predicts that the weakest player is isolated. Similarly, we find that in exclusive membership game, every structure can emerge in equilibrium but the weakest player is isolated in the strong equilibrium. Validating game-theoretic models of terrorism: insights from machine learning https://zbmath.org/1485.91010 2022-06-24T15:10:38.853281Z "Bang, James T." https://zbmath.org/authors/?q=ai:bang.james-t "Basuchoudhary, Atin" https://zbmath.org/authors/?q=ai:basuchoudhary.atin "Mitra, Aniruddha" https://zbmath.org/authors/?q=ai:mitra.aniruddha (no abstract) Subgame-perfect equilibrium in games with almost perfect information: dispensing with public randomization https://zbmath.org/1485.91011 2022-06-24T15:10:38.853281Z "Barelli, Paulo" https://zbmath.org/authors/?q=ai:barelli.paulo "Duggan, John" https://zbmath.org/authors/?q=ai:duggan.john Summary: [\textit{C. Harris} et al., Econometrica 63, No. 3, 507--544 (1995; Zbl 0839.90147)] added a public randomization device to dynamic games with almost perfect information to ensure existence of subgame perfect equilibria (SPE). We show that when Nature's moves are atomless in the original game, public randomization does not enlarge the set of SPE payoffs: any SPE obtained using public randomization can be decorrelated'' to produce a payoff-equivalent SPE of the original game. As a corollary, we provide an alternative route to a result of [\textit{W. He} and \textit{Y. Sun}, Theor. Econ. 15, No. 2, 811--859 (2020; Zbl 1466.91034)] on existence of SPE without public randomization, which in turn yields equilibrium existence for stochastic games with weakly continuous state transitions. Delegation and ambiguity in correlated equilibrium https://zbmath.org/1485.91012 2022-06-24T15:10:38.853281Z "Grant, Simon" https://zbmath.org/authors/?q=ai:grant.simon "Stauber, Ronald" https://zbmath.org/authors/?q=ai:stauber.ronald Summary: In the context of normal-form games with complete information, we introduce a notion of correlated equilibrium that allows partial delegation to a mediator and ambiguity in the correlation device. Without ambiguity, the sets of equilibrium action distributions are equivalent to those for coarse correlated equilibrium [\textit{H. Moulin} and \textit{J. P. Vial}, Int. J. Game Theory 7, 201--221 (1978; Zbl 0419.90087)]. With correlation devices that incorporate ambiguity, any action distribution that Pareto dominates a coarse correlated equilibrium or a correlated equilibrium [\textit{R. J. Aumann}, J. Math. Econ. 1, 67--96 (1974; Zbl 0297.90106)], can be approximated with an arbitrary degree of precision using the proposed equilibrium notion. These approximations are attained in one-shot, static strategic interactions, and do not require repeated play. We also analyze such equilibria when the set of feasible posteriors is exogenously constrained, which yields, as a special case, a definition and characterization of an ambiguous correlated equilibrium'' that does \textit{not} require delegation to the mediator. Self-organizing collective action: group dynamics by collective reputation https://zbmath.org/1485.91013 2022-06-24T15:10:38.853281Z "Obayashi, Shinya" https://zbmath.org/authors/?q=ai:obayashi.shinya Summary: This paper analyzes the dynamics of collective action through collective reputation, which indicates the extent to which groups succeed. Many previous works introduced psychological traits such as irrationality and a sense of fairness to explain the diffusion of collective action. However, this paper analyzes the relationship between cooperation and dynamic change in group size using game-theoretic models. The results show the sets of parameters in which positive feedback between cooperation and group size occurs. In these parameter sets, cooperation creates a good collective image (reputation) and encourages outsiders to join the group. In turn, the group expansion gives them incentives to cooperate. Additionally, when this positive feedback functions, punishment is found to be unnecessary for cooperation. The general graph matching game: approximate core https://zbmath.org/1485.91014 2022-06-24T15:10:38.853281Z "Vazirani, Vijay V." https://zbmath.org/authors/?q=ai:vazirani.vijay-v Summary: The classic paper of \textit{L. S. Shapley} and \textit{M. Shubik} [Int. J. Game Theory 1, 111--130 (1971; Zbl 0236.90078)] characterized the core of the assignment game using ideas from matching theory and LP-duality theory and their highly non-trivial interplay. Whereas the core of this game is always non-empty, that of the general graph matching game can be empty. This paper salvages the situation by giving an imputation in the 2/3-approximate core for the latter; moreover this imputation can be computed in polynomial time. This bound is best possible, since it is the integrality gap of the natural underlying LP. Our profit allocation method goes further: the multiplier on the profit of an agent is often better than $$\frac{2}{3}$$ and lies in the interval $$[\frac{2}{3},1]$$, depending on how severely constrained the agent is. The evolution of networks and local public good provision: a potential approach https://zbmath.org/1485.91015 2022-06-24T15:10:38.853281Z "Kinateder, Markus" https://zbmath.org/authors/?q=ai:kinateder.markus "Merlino, Luca Paolo" https://zbmath.org/authors/?q=ai:merlino.luca-paolo (no abstract) How to detect a salami slicer: a stochastic controller-and-stopper game with unknown competition https://zbmath.org/1485.91016 2022-06-24T15:10:38.853281Z "Ekström, Erik" https://zbmath.org/authors/?q=ai:ekstrom.erik "Lindensjö, Kristoffer" https://zbmath.org/authors/?q=ai:lindensjo.kristoffer "Olofsson, Marcus" https://zbmath.org/authors/?q=ai:olofsson.marcus Coalitional bargaining games: a new concept of value and coalition formation https://zbmath.org/1485.91017 2022-06-24T15:10:38.853281Z "Gomes, Armando" https://zbmath.org/authors/?q=ai:gomes.armando Summary: We propose a new solution for coalition bargaining problems among $$n$$ players that can form coalitions \textsc{c} generating heterogenous coalitional values $$s_{\mathsf{c}}\in R$$. The players' values $$\nu_i$$ and probability of coalition formation $$\mu_{\mathsf{c}}$$ are given by: $\nu_i=\sum\limits_{\mathsf{c}\in W}(\delta \nu_i+\gamma)I(i\in\mathsf{c})\mu_{\mathsf{c}}\text{ and }\sum\limits_{\mathsf{c}\in W}\mu_{\mathsf{c}}=1,$ where coalition \textsc{c} is chosen only if it maximizes the average gain $$\gamma_{\mathsf{c}}=\frac{1}{|\mathsf{c}|}\left(s_{\mathsf{c}}-\delta\sum_{j\in\mathsf{c}}\nu_j\right)$$ and $$\gamma\equiv\max_{\mathsf{c}\in W}\gamma_{\mathsf{c}}$$. This solution is the strong Markov perfect equilibrium of a non-cooperative coalition bargaining game where players choose simultaneously the coalition they want to join followed by negotiations to split the surplus. The solution does not rely on the specification of a proposer recognition protocol. For majority voting games, the solution exhibits more inequality among the values of large and small parties and a concentrated equilibrium coalition formation distribution. Corrections to: Nash equilibrium in a special case of symmetric resource extraction games'' https://zbmath.org/1485.91018 2022-06-24T15:10:38.853281Z "Sylenko, I. V." https://zbmath.org/authors/?q=ai:sylenko.i-v Correction to the author's article [Cybern. Syst. Anal. 57, No. 5, 809--819 (2021; Zbl 1479.91033); translation from Kibern. Sist. Anal. 57, No. 5, 156--167 (2021)]. Rates of convergence for the policy iteration method for mean field games systems https://zbmath.org/1485.91019 2022-06-24T15:10:38.853281Z "Camilli, Fabio" https://zbmath.org/authors/?q=ai:camilli.fabio "Tang, Qing" https://zbmath.org/authors/?q=ai:tang.qing Summary: Convergence of the policy iteration method for discrete and continuous optimal control problems holds under general assumptions. Moreover, in some circumstances, it is also possible to show a quadratic rate of convergence for the algorithm. For mean field games, convergence of the policy iteration method has been recently proved in [\textit{S. Cacace} et al., ESAIM, Control Optim. Calc. Var. 27, Paper No. 85, 19 p. (2021; Zbl 1473.49043)]. Here, we provide an estimate of its rate of convergence. Submodular mean field games: existence and approximation of solutions https://zbmath.org/1485.91020 2022-06-24T15:10:38.853281Z "Dianetti, Jodi" https://zbmath.org/authors/?q=ai:dianetti.jodi "Ferrari, Giorgio" https://zbmath.org/authors/?q=ai:ferrari.giorgio "Fischer, Markus" https://zbmath.org/authors/?q=ai:fischer.markus|fischer.markus.1 "Nendel, Max" https://zbmath.org/authors/?q=ai:nendel.max Summary: We study mean field games with scalar Itô-type dynamics and costs that are \textit{submodular} with respect to a suitable order relation on the state and measure space. The submodularity assumption has a number of interesting consequences. First, it allows us to prove existence of solutions via an application of Tarski's fixed point theorem, covering cases with discontinuous dependence on the measure variable. Second, it ensures that the set of solutions enjoys a lattice structure: in particular, there exist minimal and maximal solutions. Third, it guarantees that those two solutions can be obtained through a simple learning procedure based on the iterations of the best-response-map. The mean field game is first defined over ordinary stochastic controls, then extended to relaxed controls. Our approach also allows us to prove existence of a strong solution for a class of submodular mean field games with common noise, where the representative player at equilibrium interacts with the (conditional) mean of its state's distribution. Group extinction in iterated two person games with evolved group-level mixed strategies https://zbmath.org/1485.91021 2022-06-24T15:10:38.853281Z "Bradford, R. A. W." https://zbmath.org/authors/?q=ai:bradford.r-a-w Summary: The shift to a genetic basis of evolution in the 1960s, and away from group selection, created a problem in regard to the origin of cooperative behavior in human societies. The resolution essentially involves mutual recognition of individuals, thus permitting the phenomena of reputation, reciprocation, and retribution to arise, these being key to stable cooperative societies. The analysis presented, based on evolutionary game theory, serves to emphasize the crucial role of individual recognition by illustrating the consequences of assuming the opposite. It is shown that where tribal membership is apparent, but individuals are not recognizable, evolving mistrust leads to tribal extinction in an evolutionary game theory model. Moreover, a single tribe is also unstable to schism. Subsequently, the extinction of one schismatic group occurs. Failure to recognize individuals therefore facilitates a mechanism which leads to increasing conformity. Iterated prisoner's dilemma among mobile agents performing 2D random walk https://zbmath.org/1485.91022 2022-06-24T15:10:38.853281Z "Hižak, Jurica" https://zbmath.org/authors/?q=ai:hizak.jurica Summary: When iterated prisoner's dilemma takes place on a two-dimensional plane among mobile agents, the course of the game slightly differs from that one in a well-mixed population. In this paper we present a detailed derivation of the expected number of encounters required for tit-for-tat strategy to get even with always-defect strategy in a Brownian-like population. It will be shown that in such an environment tit-for-tat can perform better than in a well-mixed population. The survival of inefficient and efficient norms: equilibria with and without meta-norms in a repeated norm enforcing game https://zbmath.org/1485.91023 2022-06-24T15:10:38.853281Z "Kira, Yosuke" https://zbmath.org/authors/?q=ai:kira.yosuke Summary: Although meta-norms have been considered as the key to sustaining cooperation norms, this study argues that the meta-norms also facilitate the survival of inefficient norms. The opportunistic norm violation strategy is proposed as an alternative mechanism to motivate costly punishments. A repeated norm enforcing game, in which the externality of the normative action can be negative or positive, is analyzed. This game is equivalent to a social dilemma if the externality is large enough. The ranges of externalities that support tit-for-tat, meta-norm, and opportunism equilibria are compared. The meta-norm equilibrium has the highest stability; however, it can persist in negative externalities. Finally, the opportunism equilibrium is more stable than the tit-for-tat equilibrium, but it breaks down when the externality is small. The reputation trap https://zbmath.org/1485.91024 2022-06-24T15:10:38.853281Z "Levine, David K." https://zbmath.org/authors/?q=ai:levine.david-k Summary: Few want to do business with a partner who has a bad reputation. Consequently, once a bad reputation is established, it can be difficult to get rid of. This leads on the one hand to the intuitive idea that a good reputation is easy to lose and hard to gain. On the other hand, it can lead to a strong form of history dependence in which a single beneficial or adverse event can cast a shadow over a very long period of time. It gives rise to a reputational trap where an agent rationally chooses not to invest in a good reputation because the chances others will find out is too low. Nevertheless, the same agent with a good reputation will make every effort to maintain it. Here, a simple reputational model is constructed and the conditions for there to be a unique equilibrium that constitutes a reputation trap are characterized. Evolutionary dynamics of cooperation in the $$N$$-person stag hunt game https://zbmath.org/1485.91025 2022-06-24T15:10:38.853281Z "Luo, Qin" https://zbmath.org/authors/?q=ai:luo.qin "Liu, Linjie" https://zbmath.org/authors/?q=ai:liu.linjie "Chen, Xiaojie" https://zbmath.org/authors/?q=ai:chen.xiaojie Summary: In this paper, we consider the $$N$$-person stag hunt game based on the two-person stag hunt game and assume that the payoff of successful stag hunters is larger than that of hare hunters, which is an important feature of the game, but is often ignored in previous works. We first study the evolutionary dynamics of cooperation for the game in infinite well-mixed populations by using the replicator equation, and find that there always exists only one interior equilibrium which is unstable. We then investigate the game in finite well-mixed populations by applying the Markov process, and observe that the equation of gradient of selection always has a unique interior root, which is consistent with the finding in infinite populations. We finally consider the game in structured populations by means of the pair approximation approach. We accordingly obtain the dynamical equation for weak selection to depict the evolutionary dynamics of cooperation in structured populations, and find that there still exists the case in which there is only one interior unstable equilibrium. Our work unveils the universal characteristics of cooperative dynamics in different scenarios for the $$N$$-person stag hunt game. Competing conventions with costly information acquisition https://zbmath.org/1485.91026 2022-06-24T15:10:38.853281Z "Rozzi, Roberto" https://zbmath.org/authors/?q=ai:rozzi.roberto (no abstract) High-reputation individuals exert greater influence on cooperation in spatial public goods game https://zbmath.org/1485.91027 2022-06-24T15:10:38.853281Z "Shen, Yong" https://zbmath.org/authors/?q=ai:shen.yong "Yin, Weikang" https://zbmath.org/authors/?q=ai:yin.weikang "Kang, Hongwei" https://zbmath.org/authors/?q=ai:kang.hongwei "Zhang, Haigang" https://zbmath.org/authors/?q=ai:zhang.haigang "Wang, Mie" https://zbmath.org/authors/?q=ai:wang.mie Summary: Using reputation and payoff fusion information as a strategy update rule has been demonstrated to improve the level of cooperation. Individuals with relatively high reputations tend to have a relatively high influence on cooperation. Based on this idea, this study expanded the influence range of individuals with a relatively high reputation. We explored the impact of the above changes on cooperation evolution in a spatial public goods game that uses reputation and payoff fusion information as a strategy update rule. The results showed that expanding the range of influence of individuals with a relatively high reputation improved the cooperative level of the population when the reputation weight, $$\omega$$, was moderate. However, when $$\omega$$ was small, expanding the range of relatively high-reputation individuals' influence decreased the cooperative level of the population. We also analyzed fluctuations in the cooperative evolution process and its evolutionary causes. Two game-theoretic problems of approach https://zbmath.org/1485.91028 2022-06-24T15:10:38.853281Z "Ershov, A. A." https://zbmath.org/authors/?q=ai:ershov.aleksandr-anatolevich "Ushakov, A. V." https://zbmath.org/authors/?q=ai:ushakov.andrej-v "Ushakov, V. N." https://zbmath.org/authors/?q=ai:ushakov.vladimir-nikolaevich Robust dynamic programming in $$N$$ players uncertain differential games https://zbmath.org/1485.91029 2022-06-24T15:10:38.853281Z "Jiménez-Lizárraga, Manuel" https://zbmath.org/authors/?q=ai:jimenez-lizarraga.manuel "Rodríguez-Sánchez, Sara V." https://zbmath.org/authors/?q=ai:rodriguez-sanchez.sara-veronica "De La Cruz, Naín" https://zbmath.org/authors/?q=ai:de-la-cruz.nain "Villarreal, César Emilio" https://zbmath.org/authors/?q=ai:villarreal.cesar-emilio Summary: In this paper we consider a non-cooperative $$N$$ players differential game affected by deterministic uncertainties. Sufficient conditions for the existence of a robust feedback Nash equilibrium are presented in a set of min-max forms of Hamilton-Jacobi-Bellman equations. Such conditions are then used to find the robust Nash controls for a linear affine quadratic game affected by a square integrable uncertainty, which is seen as a malicious fictitious player trying to maximize the cost function of each player. The approach allows us to find robust strategies in the solution of a group of coupled Riccati differential equation. The finite, as well as infinite, time horizon cases are solved for this last game. As an illustration of the approach, the problem of the coordination of a two-echelon supply chain with seasonal uncertain fluctuations in demand is developed. Altruistic-like equilibrium in a differential game of renewable resource extraction https://zbmath.org/1485.91030 2022-06-24T15:10:38.853281Z "Mazalov, Vladimir" https://zbmath.org/authors/?q=ai:mazalov.vladimir-viktorovich "Parilina, Elena" https://zbmath.org/authors/?q=ai:parilina.elena-m "Zhou, Jiangjing" https://zbmath.org/authors/?q=ai:zhou.jiangjing Summary: We consider a model of renewable resource extraction described by a differential game with infinite horizon. The environmental problems are often considered from cooperative prospective as selfish behavior of the players may negatively affects not only on other players' profits, but also on the environment. The reason is the joint stock of resource which is influenced by all players. We characterize the Berge and altruistic equilibrium in a differential game of renewable resource extraction and compare them with the Nash equilibrium. According to the concept of altruistic equilibrium players can choose the part of the other players' payoffs they support and summarize with the part of their own profit. This equilibrium can be considered as an intermediate between Berge and Nash equilibria. We make numerical simulations and demonstrate theoretical results for the case of $$n$$ symmetric players. For the entire collection see [Zbl 1482.90002]. A discrete game problem with a non-convex terminal set and a possible breakdown in dynamics https://zbmath.org/1485.91031 2022-06-24T15:10:38.853281Z "Izmest'ev, Igor' V." https://zbmath.org/authors/?q=ai:izmestev.igor-vyacheslavovich "Ukhobotov, Viktor I." https://zbmath.org/authors/?q=ai:ukhobotov.viktor-ivanovich Summary: A one-dimensional discrete game problem with a given endpoint is considered. A terminal set is a union of an infinite number of disjoint segments of equal length. This terminal set has the meaning of the neighborhood of the desired state of the system, taking into account the periodicity. It is believed that one breakdown is possible, which leads to a change in the dynamics of the controlled process. The breakdown time is not known in advance. The first player's control is based on the principle of minimizing the guaranteed result. The opposite side is the second player and the moment of the breakdown. In this paper, we have found necessary and sufficient termination conditions and constructed the corresponding controls of the players. As an example, we consider the problem of controlling a rotational mechanical system with disturbance and possible breakdown. For the entire collection see [Zbl 1482.90002]. Imposing equilibrium restrictions in the estimation of dynamic discrete games https://zbmath.org/1485.91032 2022-06-24T15:10:38.853281Z "Aguirregabiria, Victor" https://zbmath.org/authors/?q=ai:aguirregabiria.victor "Marcoux, Mathieu" https://zbmath.org/authors/?q=ai:marcoux.mathieu Summary: Imposing equilibrium restrictions provides substantial gains in the estimation of dynamic discrete games. Estimation algorithms imposing these restrictions have different merits and limitations. Algorithms that guarantee local convergence typically require the approximation of high-dimensional Jacobians. Alternatively, the nested pseudo-likelihood (NPL) algorithm is a fixed-point iterative procedure, which avoids the computation of these matrices, but -- in games -- may fail to converge to the consistent NPL estimator. In order to better capture the effect of iterating the NPL algorithm in finite samples, we study the asymptotic properties of this algorithm for data generating processes that are in a neighborhood of the NPL fixed-point stability threshold. We find that there are always samples for which the algorithm fails to converge, and this introduces a selection bias. We also propose a spectral algorithm to compute the NPL estimator. This algorithm satisfies local convergence and avoids the approximation of Jacobian matrices. We present simulation evidence and an empirical application illustrating our theoretical results and the good properties of the spectral algorithm. Multicriteria dynamic games with random horizon https://zbmath.org/1485.91033 2022-06-24T15:10:38.853281Z "Rettieva, Anna" https://zbmath.org/authors/?q=ai:rettieva.anna-n Summary: We consider a dynamic, discrete-time, game model where the players use a common resource and have different criteria to optimize. Moreover, the planning horizon is assumed to be random. To construct a multicriteria Nash equilibrium the bargaining solution is adopted. To obtain a multicriteria cooperative equilibrium, a modified bargaining scheme that guarantees the fulfillment of rationality conditions is applied. To stabilize the multicriteria cooperative solution a time-consistent payoff distribution procedure is constructed. To illustrate the presented approaches, a dynamic bi-criteria bioresource management problem with many players and random planning horizon is investigated. For the entire collection see [Zbl 1482.90002]. $$Q$$-learning in a stochastic Stackelberg game between an uninformed leader and a naive follower https://zbmath.org/1485.91034 2022-06-24T15:10:38.853281Z "Rokhlin, D. B." https://zbmath.org/authors/?q=ai:rokhlin.dmitry-b Melioration learning in iterated public goods games: the impact of exploratory noise https://zbmath.org/1485.91035 2022-06-24T15:10:38.853281Z "Zschache, Johannes" https://zbmath.org/authors/?q=ai:zschache.johannes Summary: Experimental observations in iterated public goods games are explained by a simple but empirically well-grounded model of long-term reinforcement learning. In many experiments, medium levels of cooperation at the beginning decrease with further repetitions. However, in some settings, the actors only slowly learn the individual benefits of defection. In the present model, the decay in cooperation is mitigated by high individual returns, a large group size or stability in the group's composition. Results from agent-based simulations are presented, and the underlying mechanisms are disclosed. The proposed explanation stresses the role of exploratory noise: if multiple actors explore their alternatives simultaneously, the marginal benefit of defection diminishes and cooperation can be sustained. Informational robustness of common belief in rationality https://zbmath.org/1485.91036 2022-06-24T15:10:38.853281Z "Ziegler, Gabriel" https://zbmath.org/authors/?q=ai:ziegler.gabriel Summary: In this note, I explore the implications of informational robustness under the assumption of common belief in rationality. That is, predictions for incomplete-information games which are valid across all possible information structures. First, I address this question from a global perspective and then generalize the analysis to allow for localized informational robustness. Relational communication https://zbmath.org/1485.91037 2022-06-24T15:10:38.853281Z "Kolotilin, Anton" https://zbmath.org/authors/?q=ai:kolotilin.anton "Li, Hongyi" https://zbmath.org/authors/?q=ai:li.hongyi Summary: We study a communication game between an informed sender and an uninformed receiver with repeated interactions and voluntary transfers. Transfers motivate the receiver's decision-making and signal the sender's information. Although full separation can always be supported in equilibrium, partial or complete pooling is optimal if the receiver's decision-making is highly responsive to information. In this case, the receiver's decision-making is disciplined by pooling states where she is most tempted to defect. Correction to: Bayesian persuasion under partial commitment'' https://zbmath.org/1485.91038 2022-06-24T15:10:38.853281Z "Min, Daehong" https://zbmath.org/authors/?q=ai:min.daehong The omitted content of Footnote 17 in the author's paper [ibid. 72, No. 3, 743--764 (2021; Zbl 1482.91042)] is given. Correction of dynamical network's viability by decentralization by price https://zbmath.org/1485.91039 2022-06-24T15:10:38.853281Z "Galina, Vinogradova" https://zbmath.org/authors/?q=ai:galina.vinogradova Summary: A connectionist system of a finite set of autonomous agents evolving independently over a common centralized environment of scarce resources is discussed and connected with the results of the agents' interactions by the connection operator, also evolving independently. The system forms a dynamical network. \par The network is viable if a joint evolution satisfies the centralized scarcity constraints set by the environment. The focus of this paper is on the problem of restoring the network's viability, which is intrinsic as the decentralized behaviors (dynamics) of the agents and of the connection operator are not necessarily consistent with the centralized constraints. For restoring the viability, the decentralized dynamics are corrected using viability multipliers, which are regarded as correction prices. The correction prices provide the information about changes in the dynamics, necessary to govern evolutions satisfying the constraints. In this aspect, the viability of the network is restored by the mechanism of decentralization by price. Termination of the ice bucket challenge https://zbmath.org/1485.91040 2022-06-24T15:10:38.853281Z "Polyakov, Pavel" https://zbmath.org/authors/?q=ai:polyakov.pavel-y Summary: The ice bucket challenge is a social game aimed at encouraging donations to the amyotrophic lateral sclerosis association. The rules imply that each participant challenges each recruited follower to dump a bucket of ice water on his or her head. The network of who has nominated whom has a tree structure. The short duration of the ice bucket challenge is explained by using the reproduction number $$R_0$$, under the assumption that the capacity to recruit followers varies with the participant. The epidemic lasts until the interruption of the transmission tree occurring well before the depletion of susceptible followers. Such a tree is reconstructed from publicly available contact data and the interest in this game. Ky-Fan inequality, Nash equilibria in some idempotent and harmonic convex structure https://zbmath.org/1485.91041 2022-06-24T15:10:38.853281Z "Briec, Walter" https://zbmath.org/authors/?q=ai:briec.walter "Yesilce, Ilknur" https://zbmath.org/authors/?q=ai:yesilce.ilknur Summary: $$\mathbb{B}$$-convexity is defined as a suitable Peano-Kuratowski limit of linear convexities. An alternative idempotent convex structure called inverse $$\mathbb{B}$$-convexity was recently proposed in the literature. This paper continues and extends some investigation started in these papers. In particular we focus on the Ky-Fan inequality and prove the existence of a Nash equilibrium for inverse $$\mathbb{B}$$-convex games. This we do by considering a suitable harmonic'' topological structure which allows to establish a KKM theorem as well as some important related properties. Among other things a coincidence theorem is established. The paper also establishes fixed point results and Nash equilibriums properties in the case where two different convex topological structures are merged. It follows that one can consider a large class of games where the players may optimize their payoff subject to different forms of convexity. Among other things an inverse $$\mathbb{B}$$-convex version of the Debreu-Gale-Nikaido theorem is proposed. Good properties of combinatorial rulesets: some consequences https://zbmath.org/1485.91042 2022-06-24T15:10:38.853281Z "Carvalho, Alda" https://zbmath.org/authors/?q=ai:carvalho.alda "Santos, Carlos" https://zbmath.org/authors/?q=ai:santos.carlos-p "Neto, João" https://zbmath.org/authors/?q=ai:neto.joao "Silva, Jorge Nuno" https://zbmath.org/authors/?q=ai:silva.jorge-nuno-o Summary: In 2000, \textit{M. Thompson} published the very interesting paper [Defining the Abstract'', Games J. (2000), \url{http://www.thegamesjournal.com/articles/DefiningtheAbstract.shtml}] enumerating some properties that good rulesets' should have. Good ruleset' in Thompson's text meant nice to play' (enjoyable, challenging, addictive). In this paper we will extend Thompson's ideas. We will also show how Ludus Association (Ludus) organised competitions, materials and technologic tools using these good rulesets'. For the entire collection see [Zbl 1280.00097]. A curricular application: the game of parallel https://zbmath.org/1485.91043 2022-06-24T15:10:38.853281Z "Faria, Raquel" https://zbmath.org/authors/?q=ai:faria.raquel "Cabral, João" https://zbmath.org/authors/?q=ai:cabral.joao "Melo, Helena" https://zbmath.org/authors/?q=ai:melo.helena-sousa For the entire collection see [Zbl 1280.00097]. Computation and efficiency of potential function minimizers of combinatorial congestion games https://zbmath.org/1485.91044 2022-06-24T15:10:38.853281Z "Kleer, Pieter" https://zbmath.org/authors/?q=ai:kleer.pieter "Schäfer, Guido" https://zbmath.org/authors/?q=ai:schafer.guido Authors' abstract: We study the computation and efficiency of pure Nash equilibria in combinatorial congestion games, where the strategies of each player $$i$$ are given by the binary vectors of a polytope $$P_i$$. Our main goal is to understand which structural properties of such polytopal congestion games enable us to derive an efficient equilibrium selection procedure to compute pure Nash equilibria with attractive social cost approximation guarantees. To this aim, we identify two general properties of the underlying aggregation polytope $$P_N=\sum_i P_i$$ which are sufficient for our results to go through, namely the integer decomposition property (IDP) and the box-totally dual integrality property (box-TDI). Our main results for polytopal congestion games satisfying IDP and box-TDI are as follows: (i) we show that pure Nash equilibria can be computed in polynomial time. In fact, we obtain this result through a general framework for separable convex function minimization, which might be of independent interest. (ii) We bound the inefficiency of these equilibria and show that this provides a tight bound on the price of stability. (iii) We also prove that these results extend to strong equilibria for the bottleneck variant'' of polytopal congestion games. Examples of polytopal congestion games satisfying IDP and box-TDI include common source network congestion games, symmetric totally unimodular congestion games, non-symmetric matroid congestion games and symmetric matroid intersection congestion games (in particular, $$r$$-arborescences and strongly base-orderable matroids). Reviewer: Michel Rigo (Liège) How strong can the Parrondo effect be? II https://zbmath.org/1485.91045 2022-06-24T15:10:38.853281Z "Ethier, S. N." https://zbmath.org/authors/?q=ai:ethier.stewart-n "Lee, Jiyeon" https://zbmath.org/authors/?q=ai:lee.jiyeon Summary: Parrondo's coin-tossing games comprise two games, $$A$$ and $$B$$. The result of game $$A$$ is determined by the toss of a fair coin. The result of game $$B$$ is determined by the toss of a $$p_0$$-coin if capital is a multiple of $$r$$, and by the toss of a $$p_1$$-coin otherwise. In either game, the player wins one unit with heads and loses one unit with tails. Game $$B$$ is fair if $$(1-p_0)(1-p_1)^{r-1}=p_0\,p_1^{r-1}$$. In a previous paper we showed that, if the parameters of game $$B$$, namely $$r, p_0$$, and $$p_1$$, are allowed to be arbitrary, subject to the fairness constraint, and if the two (fair) games $$A$$ and $$B$$ are played in an arbitrary periodic sequence, then the rate of profit can not only be positive (the so-called Parrondo effect), but also be arbitrarily close to 1 (i.e., 100\%). Here we prove the same conclusion for a random sequence of the two games instead of a periodic one, that is, at each turn game $$A$$ is played with probability $$\gamma$$ and game $$B$$ is played otherwise, where $$\gamma\in (0,1)$$ is arbitrary. For Part I see [Zbl 1427.60152]. For the entire collection see [Zbl 07455846]. Bold play and timid play with multiple payoffs https://zbmath.org/1485.91046 2022-06-24T15:10:38.853281Z "Serpa, Cristina" https://zbmath.org/authors/?q=ai:serpa.cristina "Buescu, Jorge" https://zbmath.org/authors/?q=ai:buescu.jorge Summary: We extend the concept of bold play in gambling, where the game has a unique win payoff (it returns twice the original wager). We model a game where the player can bet all his money in each stake. The probability that a gambler reaches his goal using the bold play strategy is the solution of a functional equation. We also consider the timid play strategy in which the bet in each stake is always the same regardless the amount of money the gambler has. We refer to the game of scratch cards where is impossible a gambler playing a bold play strategy (for simple or multiple payoffs).\par In this paper we first introduce the classical game strategy called bold play and then extend this concept introducing a multiple set of payoffs for the game. We also introduce the classical timid play strategy and extend it similarly to a multiple set of payoffs. For the entire collection see [Zbl 1360.00138]. Team players: how social skills improve team performance https://zbmath.org/1485.91047 2022-06-24T15:10:38.853281Z "Weidmann, Ben" https://zbmath.org/authors/?q=ai:weidmann.ben "Deming, David J." https://zbmath.org/authors/?q=ai:deming.david-j Summary: Most jobs require teamwork. Are some people good team players? In this paper, we design and test a new method for identifying individual contributions to team production. We randomly assign people to multiple teams and predict team performance based on previously assessed individual skills. Some people consistently cause their team to exceed its predicted performance. We call these individuals team players''. Team players score significantly higher on a well-established measure of social intelligence, but do not differ across a variety of other dimensions, including IQ, personality, education, and gender. Social skills -- defined as a single latent factor that combines social intelligence scores with the team player effect -- improve team performance about as much as IQ. We find suggestive evidence that team players increase effort among teammates. Does the approval mechanism induce the efficient extraction in common pool resource games? https://zbmath.org/1485.91048 2022-06-24T15:10:38.853281Z "Yao, Koffi Serge William" https://zbmath.org/authors/?q=ai:yao.koffi-serge-william "Lavaine, Emmanuelle" https://zbmath.org/authors/?q=ai:lavaine.emmanuelle "Willinger, Marc" https://zbmath.org/authors/?q=ai:willinger.marc Summary: \textit{T. Masuda} et al. [Games Econ. Behav. 83, 73--85 (2014; Zbl 1284.91153)] showed that the minimum approval mechanism (AM) implements the efficient level of public good theoretically and experimentally in a linear public good game. We extent this result to a two-players common pool resource (CPR) game. The AM adds a second stage into the extraction game. In the first stage, each group member proposes his level of extraction. In the second stage, the proposed extractions and associated payoffs are displayed and each player is asked to approve or to disapprove both proposed extractions. If both players approve, the proposals are implemented. Otherwise, a uniform level of extraction, the \textit{disapproval benchmark} (\textit{DB}), is imposed onto each player. We consider three different \textit{DB}s: the minimum proposal (\textit{MIN}), the maximum proposal (\textit{MAX}) and the Nash extraction level (\textit{NASH}). We derive theoretical predictions for each \textit{DB} following backward elimination of weakly dominated strategies (\textit{BEWDS}). We first underline the strength of the AM, by showing that the \textit{MIN} implements the optimum theoretically and experimentally. The sub-games predicted under the \textit{NASH} are Pareto improving with respect to the Nash equilibrium. The \textit{MAX} leads, either to Pareto improving outcomes with respect to the free access extractions, or to a Pareto degradation. Our experimental results show that the \textit{MAX} and the \textit{NASH} reduce the level of over-extraction of the CPR. The \textit{MAX} leads above all to larger reductions of (proposed and realized) extractions than the \textit{NASH}. Rock-paper-scissors play: beyond the win-stay/lose-change strategy https://zbmath.org/1485.91049 2022-06-24T15:10:38.853281Z "Zhang, Hanshu" https://zbmath.org/authors/?q=ai:zhang.hanshu "Moisan, Frederic" https://zbmath.org/authors/?q=ai:moisan.frederic "Gonzalez, Cleotilde" https://zbmath.org/authors/?q=ai:gonzalez.cleotilde (no abstract) Robust coalitional implementation https://zbmath.org/1485.91086 2022-06-24T15:10:38.853281Z "Guo, Huiyi" https://zbmath.org/authors/?q=ai:guo.huiyi "Yannelis, Nicholas C." https://zbmath.org/authors/?q=ai:yannelis.nicholas-constantine Summary: The paper introduces coalition structures to study belief-free full implementation. When the mechanism designer does not know which coalitions are admissible, we provide necessary and almost sufficient conditions on when a social choice function is robustly coalitionally implementable, i.e., implementable regardless of the coalition pattern and the belief structure. Robust coalitional implementation is a strong requirement that imposes stringent conditions on implementable social choice functions. However, when the mechanism designer has additional information on which coalitions are admissible, we show that coalitional manipulations may help a mechanism designer to implement social choice functions that are not robustly implementable in the sense of \textit{D. Bergemann} and \textit{S. Morris} [Rev. Econ. Stud. 76, No. 4, 1175--1204 (2009; Zbl 1187.91057); Games Econ. Behav. 71, No. 2, 261--281 (2011; Zbl 1208.91043)]. As different social choice functions are implementable under different coalition patterns, the paper provides insights on when agents should be allowed to play cooperatively. Separating the communication complexity of truthful and nontruthful algorithms for combinatorial auctions https://zbmath.org/1485.91105 2022-06-24T15:10:38.853281Z "Assadi, Sepehr" https://zbmath.org/authors/?q=ai:assadi.sepehr "Khandeparkar, Hrishikesh" https://zbmath.org/authors/?q=ai:khandeparkar.hrishikesh "Saxena, Raghuvansh R." https://zbmath.org/authors/?q=ai:saxena.raghuvansh-r "Weinberg, S. Matthew" https://zbmath.org/authors/?q=ai:weinberg.seth-matthew Coalition-then-allocation legislative bargaining https://zbmath.org/1485.91107 2022-06-24T15:10:38.853281Z "Kawamori, Tomohiko" https://zbmath.org/authors/?q=ai:kawamori.tomohiko Summary: We investigate legislative bargaining where players first bargain over coalitions and after one coalition is formed, players in this coalition bargain over allocations. We show that if discount factors in coalition bargaining are smaller than those in allocation bargaining and sufficiently large, in any stationary subgame perfect equilibrium (SSPE), relatively impatient proposers immediately form a minimal winning coalition of relatively impatient players, but relatively patient proposers fail to form a coalition and bargaining delays occur. We also show that if the discount factors in coalition bargaining are smaller than those in allocation bargaining and sufficiently small, delays do not occur. Furthermore, we show that if the discount factors in allocation bargaining are smaller than those in coalition bargaining and sufficiently similar across players, there exist multiple SSPEs exhibiting delays and having different payoff tuples. We also introduce leader-dependent hedonic games, where each player has a preference relation over pairs of a coalition and its leader. We view a truncated game with replacing subgames of allocation bargaining by their SSPE playoff tuples to be based on a leader-dependent hedonic game. Resource allocation based on DEA and non-cooperative game https://zbmath.org/1485.91109 2022-06-24T15:10:38.853281Z "Wang, Menghan" https://zbmath.org/authors/?q=ai:wang.menghan "Li, Lin" https://zbmath.org/authors/?q=ai:li.lin.2|li.lin.1|li.lin "Dai, Qianzhi" https://zbmath.org/authors/?q=ai:dai.qianzhi "Shi, Fangnan" https://zbmath.org/authors/?q=ai:shi.fangnan Summary: Resource allocation is one of the most important applications of data envelopment analysis (DEA). Usually, the resource to be allocated is directly related to the interests of decision-making units (DMUs), thus the dynamic non-cooperative game is one of the representative behaviours in the allocation process. However, it is rarely considered in the previous DEA-based allocation studies, which may reduce the acceptability of the allocation plan. Therefore, this paper proposes a DEA-based resource allocation method considering the dynamic non-cooperative game behaviours of DMUs. The authors first deduce the efficient allocation set under the framework of variable return to scale (VRS) and build the allocation model subjecting to the allocation set. Then an iteration algorithm based on the concept of the non-cooperative game is provided for generating the optimal allocation plan. Several interesting characteristics of the algorithm are proved, including i) the algorithm is convergent, ii) the optimal allocation plan is a unique Nash equilibrium point, and iii) the optimal allocation plan is unique no matter which positive value the initial allocation takes. Some advantages of the allocation plan have been found. For example, the allocation plan is more balanced, has more incentives and less outliers, compared with other DEA-based allocation plans. Finally, the proposed method is applied to allocate the green credit among the 30 Chinese iron and steel enterprises, and the results highlight the applicability of the allocation method and solution approach. Therefore, the approach can provide decision makers with a useful resource allocation tool from the perspective of dynamic non-cooperative game. A new allocation rule for the housing market problem with ties https://zbmath.org/1485.91110 2022-06-24T15:10:38.853281Z "Xiong, Xinsheng" https://zbmath.org/authors/?q=ai:xiong.xinsheng "Wang, Xianjia" https://zbmath.org/authors/?q=ai:wang.xianjia "He, Kun" https://zbmath.org/authors/?q=ai:he.kun Summary: We address a general housing market problem with a set of agents and a set of houses. Each agent has a weak ordinal preference list that allows ties on houses as well as an initial endowment; moreover, each agent wishes to reallocate to a better house on the housing market. In this work, we reduces the complexity of the family of top trading cycles algorithms by selecting a specific house from the preferred set during the trading phase. The rule of construction digraphs is used to select an appropriate house. Based on these digraphs, we propose an extended top trading cycles algorithm with complexity $$O(n^2 r)$$, where $$n$$ is the number of agents and $$r$$ is the maximum length of ties in the preference lists. The algorithm complexity is lower than that of the state-of-the-art algorithms. We show that the proposed algorithm is individually rational, Pareto efficient, and strategy-proof. It thus overcomes the limitations of a classic top trading cycles algorithm, and features Pareto efficiency and strategy-proofness on the weak preference domain. Renegotiation of long-term contracts as part of an implicit agreement https://zbmath.org/1485.91124 2022-06-24T15:10:38.853281Z "Kostadinov, Rumen" https://zbmath.org/authors/?q=ai:kostadinov.rumen Summary: I study a repeated principal-agent game with long-term output contracts that can be renegotiated at will. Actions are observable but not contractible, so they can only be incentivized through implicit agreements formed in equilibrium. I show that contract renegotiation is a powerful tool for incentive provision, despite the stationarity of the environment. Continuation contracts are designed to punish deviations in noncontractible behavior. If the equilibrium actions are observed, these contracts are renegotiated away. This form of anticipated renegotiation results in welfare improvements over outcomes attainable by one-period contracts or by long-term contracts that are not renegotiated. When the principal is not protected by limited liability, first-best outcomes are attainable regardless of the impatience of the players. Equilibrium strategies are shown to satisfy various concepts of renegotiation-proofness. Hierarchical mean-field type control of price dynamics for electricity in smart grid https://zbmath.org/1485.91165 2022-06-24T15:10:38.853281Z "Frihi, Zahrate El Oula" https://zbmath.org/authors/?q=ai:el-oula-frihi.zahrate "Choutri, Salah Eddine" https://zbmath.org/authors/?q=ai:choutri.salah-eddine "Barreiro-Gomez, Julian" https://zbmath.org/authors/?q=ai:barreiro-gomez.julian "Tembine, Hamidou" https://zbmath.org/authors/?q=ai:tembine.hamidou Summary: This paper solves a mean-field type hierarchical optimal control problem in electricity market. The authors consider $$n-1$$ prosumers and one producer. The $$i$$th prosumer, for $$1<i<n$$, is a leader of the $$(i-1)$$th prosumer and is a follower of the $$(i+1)$$th prosumer. The first player (agent) is the follower at the bottom whereas the $$n$$th is the leader at the top. The problem is described by a linear jump-diffusion system of conditional mean-field type, where the conditioning is with respect to common noise, and a quadratic cost functional involving, the square of the conditional expectation of the controls of the agents. The authors provide a semi-explicit solution of the corresponding mean-field-type hierarchical control problem with common noise. Finally, the authors illustrate the obtained result via a numerical example with two different scenarios. A simple model of network formation with competition effects https://zbmath.org/1485.91187 2022-06-24T15:10:38.853281Z "Hiller, Timo" https://zbmath.org/authors/?q=ai:hiller.timo Summary: This paper provides a game-theoretic model of network formation with a continuous effort choice. Efforts are strategic complements for direct neighbors in the network and display global substitution/competition effects. We show that if the parameter governing local strategic complements is larger than the one governing global strategic substitutes, then all pairwise Nash equilibrium networks are nested split graphs. We also consider the problem of a planner, who can choose effort levels and place links according to a network cost function. Again all socially optimal configurations are such that the network is a nested split graph. However, the socially optimal network may be different from equilibrium networks and efficient effort levels do not coincide with Nash equilibrium effort levels. In the presence of strategic substitutes, Nash equilibrium effort levels may be too high or too low relative to efficient effort levels. The relevant applications are crime networks and R\&D collaborations among firms, but also interbank lending and trade. The mechanics of contentious politics: an agent-based modeling approach https://zbmath.org/1485.91203 2022-06-24T15:10:38.853281Z "Dacrema, Eugenio" https://zbmath.org/authors/?q=ai:dacrema.eugenio "Benati, Stefano" https://zbmath.org/authors/?q=ai:benati.stefano Summary: Contentious politics'' has become the main label to define a wide range of previously separated fields of research encompassing topics such as collective action, radicalization, armed insurgencies, and terrorism. Over the past two decades, scholars have tried to bring these various strands together into a unified field of study. In so doing, they have developed a methodology to isolate and analyze the common social and cognitive mechanisms underlying several diverse historical phenomena such as insurgencies'', revolutions'', radicalization'', or terrorism''. A multidisciplinary approach was adopted open to contributions from diverse fields such as economics, sociology, and psychology. The aim of this paper is to add to the multidisciplinarity of the field of contentious politics (CP) and introduce the instruments of agent-based modeling and network game-theory to the study of some fundamental mechanisms analyzed within this literature. In particular, the model presented in this paper describes the dynamics of one process, here defined as the radicalization of politics'', and its main underlying mechanisms. Their mechanics are analyzed in diverse social contexts differentiated by the values of four parameters: the extent of repression, inequality, social tolerance, and interconnectivity. The model can be used to explain the basic dynamics underlying different phenomena such as the development of radicalization, populism, and popular rebellions. In the final part, different societies characterized by diverse values of the aforementioned four parameters are tested through Python simulations, thereby offering an overview of the different outcomes that the mechanics of our model can shape according to the contexts in which they operate. A stochastic Stackelberg differential reinsurance and investment game with delay in a defaultable market https://zbmath.org/1485.91206 2022-06-24T15:10:38.853281Z "Bai, Yanfei" https://zbmath.org/authors/?q=ai:bai.yanfei "Zhou, Zhongbao" https://zbmath.org/authors/?q=ai:zhou.zhongbao "Xiao, Helu" https://zbmath.org/authors/?q=ai:xiao.helu "Gao, Rui" https://zbmath.org/authors/?q=ai:gao.rui "Zhong, Feimin" https://zbmath.org/authors/?q=ai:zhong.feimin Summary: In this paper, we investigate a stochastic Stackelberg differential reinsurance and investment game problem with delay for a reinsurer and an insurer in a defaultable market, which consists of a risk-free asset, a risky asset and a defaultable bond. As the leader, the reinsurer can determine reinsurance premium price and investment strategy to maximize the expected exponential utility of its terminal wealth with delay. As the follower, the insurer can select reinsurance proportion and investment strategy to maximize the expected exponential utility of its terminal wealth with delay. By using the idea of backward induction and the dynamic programming approach, we solve the leader's and follower's optimization problems sequentially and derive the Stackelberg equilibrium strategy explicitly. Then, we provide the corresponding verification theorem. Finally, we present some numerical examples to illustrate the influence of model parameters on the equilibrium strategy and draw some economic interpretations from these results. We find that the pre-default value functions are higher than the post-default value functions and the influence of delay weight on equilibrium strategy depends on the length of delay time. Moreover, when the Stackelberg equilibrium is achieved in the interior case, the optimal reinsurance premium follows the variance premium principle and the influence of delay weight on the optimal reinsurance premium strategy is just opposite to that on other strategies. Heterogeneous round-trip trading and the emergence of volatility clustering in speculation game https://zbmath.org/1485.91222 2022-06-24T15:10:38.853281Z "Katahira, Kei" https://zbmath.org/authors/?q=ai:katahira.kei "Chen, Yu" https://zbmath.org/authors/?q=ai:chen.yu.7|chen.yu.2|chen.yu.1|chen.yu.3|chen.yu.6|chen.yu.4|chen.yu.8|chen.yuqun|chen.yu.5 Summary: This study is a detailed analysis of speculation game, a simple agent-based model of financial markets, in which the round-trip trading and the dynamic wealth evolution with variable trading volumes are implemented. Instead of herding behavior, the authors find that the heterogeneous holding periods in round-trip trades can contribute to the emergence of volatility clustering. In particular, the spontaneous redistribution of market wealth through repetitions of round-trip trades with non-uniform horizons can widen the wealth disparity and establish the Pareto distribution of the capital size. As a result, the intermittent placements of relatively big orders from endogenously emerged rich traders can bring on large fluctuations in price return. Empirical data are used to support the scenario derived from the model. Evolutionarily stable strategies in stable and periodically fluctuating populations: the Rosenzweig-MacArthur predator-prey model https://zbmath.org/1485.92087 2022-06-24T15:10:38.853281Z "Grunert, Katrin" https://zbmath.org/authors/?q=ai:grunert.katrin "Holden, Helge" https://zbmath.org/authors/?q=ai:holden.helge "Stenseth, Nils Chr." https://zbmath.org/authors/?q=ai:stenseth.nils-chr (no abstract) The lower convergence tendency of imitators compared to best responders https://zbmath.org/1485.93046 2022-06-24T15:10:38.853281Z "Ramazi, Pouria" https://zbmath.org/authors/?q=ai:ramazi.pouria "Riehl, James" https://zbmath.org/authors/?q=ai:riehl.james-r "Cao, Ming" https://zbmath.org/authors/?q=ai:cao.ming Summary: Imitation is widely observed in nature and often used to model populations of decision-making agents, but it is \textit{not} yet known under what conditions a network of imitators will reach a state where they are satisfied with their decisions. We show that every network in which agents imitate the best performing strategy in their neighborhood will reach an equilibrium in finite time, provided that all agents are \textit{opponent coordinating}, i.e., earn a higher payoff if their opponent plays the same strategy as they do. It follows that any non-convergence observed in imitative networks is not necessarily a result of population heterogeneity nor special network topology, but rather must be caused by other factors such as the presence of non-opponent-coordinating agents. To strengthen this result, we show that large classes of imitative networks containing non-opponent-coordinating agents never equilibrate even when the population is homogeneous. Comparing to best-response dynamics where equilibration is guaranteed for every network of homogeneous agents playing $$2 \times 2$$ matrix games, our results imply that networks of imitators have a lower equilibration tendency. Incentive feedback Stackelberg strategy for stochastic systems with state-dependent noise https://zbmath.org/1485.93189 2022-06-24T15:10:38.853281Z "Lin, Yaning" https://zbmath.org/authors/?q=ai:lin.yaning "Gao, Wenhui" https://zbmath.org/authors/?q=ai:gao.wenhui "Zhang, Weihai" https://zbmath.org/authors/?q=ai:zhang.weihai Summary: This paper designs an incentive strategy for a class of stochastic Stackelberg games in finite horizon and infinite horizon, respectively. The obtained incentive Stackelberg strategy works well in the sense that the leader will get his desired solution in the end. Different from the existing works, the state-dependent noise is considered in the design of the incentive Stackelberg strategy. Moreover, the mean-square stabilization can be guaranteed by the follower. The algorithm procedure is put forward to obtain effectively the incentive feedback Stackelberg strategy in infinite horizon. Finally, two examples are given to shed light on the effectiveness of the proposed algorithm procedure. Nash equilibrium seeking for individual linear dynamics subject to limited communication resources https://zbmath.org/1485.93351 2022-06-24T15:10:38.853281Z "Liu, Pin" https://zbmath.org/authors/?q=ai:liu.pin "Xiao, Feng" https://zbmath.org/authors/?q=ai:xiao.feng "Wei, Bo" https://zbmath.org/authors/?q=ai:wei.bo "Yu, Mei" https://zbmath.org/authors/?q=ai:yu.mei Summary: In this paper, non-cooperative game problems with individual linear dynamics of players are addressed. In the case of limited communication resources, event-triggering mechanisms equip players to determine event instants. A period of dwell time is enforced after each event. In the dwell time, monitoring event-triggering conditions is avoided for each player, which saves resources. After the dwell time, each player triggers the broadcast to its neighbors once a fully distributed event-triggering condition is satisfied. Along this line, the Zeno behavior is excluded. The proposed control algorithm with discrete-time communications converges the systems to an NE. The effectiveness of the proposed control algorithms and event-triggering mechanisms is demonstrated through simulations. Set stability of probabilistic time-delay Boolean networks with impulsive effect https://zbmath.org/1485.93615 2022-06-24T15:10:38.853281Z "Shi, Shengnan" https://zbmath.org/authors/?q=ai:shi.shengnan "Xu, Yong" https://zbmath.org/authors/?q=ai:xu.yong.5|xu.yong.2|xu.yong.4|xu.yong.1|xu.yong.3 Summary: This paper investigates the set stability of probabilistic time-delay Boolean networks (PTDBN) with impulsive effect. Firstly, using the algebraic state space representation, an equivalent stochastic system is established for PTDBN with impulsive effect. Then, based on the probabilistic state transition matrix, a necessary and sufficient condition is presented for the set stability of PTDBN with impulsive effect. Finally, the obtained new result is applied to the networked evolutionary game with memories. Maximum principle for discrete-time stochastic optimal control problem and stochastic game https://zbmath.org/1485.93641 2022-06-24T15:10:38.853281Z "Wu, Zhen" https://zbmath.org/authors/?q=ai:wu.zhen "Zhang, Feng" https://zbmath.org/authors/?q=ai:zhang.feng Summary: This paper is first concerned with one kind of discrete-time stochastic optimal control problem with convex control domains, for which necessary condition in the form of Pontryagin's maximum principle and sufficient condition of optimality are derived. The results are then extended to two kinds of discrete-time stochastic games. Two illustrative examples are studied, for which the explicit optimal strategies are given. This paper establishes a rigorous version of discrete-time stochastic maximum principle in a clear and concise way and paves a road for further related topics.